Question

1-i
2. The argument of is ...
1+i​

Answer 1

Answer:ANSWER

Let z=

1+i

3

​

1−i

3

​

​

⇒z=

1+i

3

​

1−i

3

​

​

×

1−i

3

​

1−i

3

​

​

⇒z=

1+3

(1−i

3

​

)

2

​

⇒z=

4

1−3−2i

3

​

​

⇒z=−

2

1

​

−

2

i

3

​

​

r=

(−

2

1

​

)

2

+(−

2

3

​

​

)

2

​

=1

Comparing the above equation with z=rcosα+irsinα

rcosα=−

2

1

​

⇒cosα=−

2

1

​

rsinα=−

2

3

​

​

⇒sinα=−

2

3

​

​

Since sinα and cosα, both are negative, thus the argument will be in III

rd

quadrant.

α=180°+60°=240°(∵sin60°=

2

3

​

​

&cos60°=

2

1

​

)

Hence argument of given complex is 240

Step-by-step explanation: